Integration by parts

[mustafiz]

Can anyone tell me how to integrate the following function effectively

e^kt/(1+at)² with respect to t. Here k and a are constants.

 

[Deleted member 4993]

Can anyone tell me how to integrate the following function effectively

e^kt/(1+at)² with respect to t. Here k and a are constants.

Are you sure that you have copied the problem correctly?

The integral is not a "simple function" in real domain.

go to:

http://www.wolframalpha.com/input/?i=integrate+e^%28kt%29%2F%281%2Bat%29^2+dt

 

[mustafiz]

Are you sure that you have copied the problem correctly?

The integral is not a "simple function" in real domain.

go to:

http://www.wolframalpha.com/input/?i=integrate+e^%28kt%29%2F%281%2Bat%29^2+dt

In fact I found the integral in solving a problem:
Given, dC_A/dt = -k₁C_A² and dC_B/dt = k₁C_A²- k₂C_B; also given the condition at t = 0, C_A=C_A0 and C_B=0.
I have to find C_B(t).
What I did was, I found C_A = C_A0/(1+k₁C_A0t) from the first ODE and given condition. From the 2nd ODE and this value of C_A I found the following eqn
dC_B/dt + k₂C_B = k₁C_A0²/(1+k₁C_A0t)²; I multiplied both sides by the Integrating factor e^k₂t and upon integration found the following eqn

e^k₂tC_B = k₁C_A0² X Integration of (e^k₂t/(1+k₁C_A0t)²)dt + constant, Now I have to find the value of integral.

 

[mustafiz]

Shubhotosh,

You gave me a link that contains the solution. Could you please explain me how did you get the solution? You can email me at [deleted for security]. I would highly appreciate your response.

 

[stapel]

You gave me a link that contains the solution. Could you please explain me how did you get the solution?

The helper got the solution by entering your exercise into the Wolfram Alpha solver. The point was to show you that the equation does not have a "nice" solution.